The predator peak never coincides with the prey peak; it always arrives one beat later, because predators only multiply once prey are plentiful, and by the time predators are numerous the prey are gone. Prey birth rate, hunting efficiency and predator death rate are exactly the coefficients of the Lotka–Volterra system, and together the two populations trace a closed loop in phase space. Overhunting drives the prey extinct and takes the predators down with them; carrying capacity damps the oscillation instead.
The predator peak never coincides with the prey peak; it always arrives one beat later, because predators only multiply once prey are plentiful, and by the time predators are numerous the prey are gone. Prey birth rate, hunting efficiency and predator death rate are exactly the coefficients of the Lotka–Volterra system, and together the two populations trace a closed loop in phase space. Overhunting drives the prey extinct and takes the predators down with them; carrying capacity damps the oscillation instead.
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